ZIMSEC A Level · Physics · Form 5
Equilibrium
For a body in equilibrium: resultant force is zero and the sum of moments about any point is zero. A couple (two equal, opposite, parallel forces) produces a torque = F × perpendicular separation.
Work, energy and power
W = Fs cos θ; Ek = ½mv²; ΔEp = mgΔh; P = W/t = Fv; efficiency = useful output ÷ input.
Worked example: A car of mass 1 200 kg moves at a constant 20 m s⁻¹ against resistive forces of 600 N. Find the power output of the engine.
At constant speed, driving force = 600 N; P = Fv = 600 × 20 = 12 000 W = 12 kW
Pressure and fluids
p = ρgh; upthrust equals the weight of fluid displaced (Archimedes' principle).
Deformation of solids
- Hooke's law F = kx up to the limit of proportionality.
- Stress σ = F/A; strain ε = x/L; Young modulus E = stress ÷ strain.
- Elastic potential energy = ½Fx = ½kx² (area under force–extension graph).
- Ductile materials (copper) show plastic deformation; brittle materials (glass) break without it.
Worked example: A steel wire 2.0 m long with cross-sectional area 1.0 × 10⁻⁶ m² stretches 1.0 mm under a 100 N load. Find the Young modulus.
Stress = 100/1.0 × 10⁻⁶ = 1.0 × 10⁸ Pa; strain = 0.001/2.0 = 5.0 × 10⁻⁴
E = 1.0 × 10⁸ ÷ 5.0 × 10⁻⁴ = 2.0 × 10¹¹ Pa
Check yourself
- Find the work done by a 50 N force moving an object 4 m at 60° to the force.
- Find the energy stored in a spring of k = 200 N m⁻¹ stretched 0.10 m.
- Define the Young modulus.
Show answers
- 50 × 4 × cos 60° = 100 J
- ½ × 200 × 0.01 = 1.0 J
- The ratio of tensile stress to tensile strain (within the limit of proportionality).
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